# Risk Assessment of Polish Joint Stock Companies: Prediction of Penalties or Compensation Payments

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Analysis of Variables

#### 3.2. Sample Selection for the Modelling Process

#### 3.3. Supervised Learning

#### 3.4. Model Evaluation and Interpretation (SHAP Approach)

## 4. Results

#### 4.1. Description of Data

#### 4.1.1. Dependent Variable

#### 4.1.2. Independent Variables

#### 4.2. Analysis of Independent Variables

#### 4.3. Correlation Analysis

- Step 1: Similar to the case of X12, the X2 variable correlated in accordance with the approved threshold with three other variables. There was also a strong correlation between X12 and X2, but X2 had a lower impact on the dependent variable than X12 based on the value of the Phi coefficient;
- Step 2: the X7 and X12 variables correlated in accordance with the approved threshold with two other variables;
- Step 3: X9 correlated with one variable (labelled X10), but its correlation with the dependent variable based on the value of the Phi coefficient was weaker than for X10.

#### 4.4. Division of Data into a Training Set and a Test Set

- I group: <minimum value; I quartile>
- II group: (I quartile; median>
- III group: (median; III quartile>
- IV group: (III quartile; maximum value>

#### 4.5. Supervised Learning

## 5. Discussion

## 6. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | Elektrobudowa SA financial situation (in Polish) is available on: https://www.rynekelektryczny.pl/spor-elektrobudowy-i-orlenu-dotyczacy-metatezy/ (accessed on 21 January 2022). |

2 | Documentations of these libraries are available on the official websites dedicated to these packages: https://scikit-learn.org/stable/index.html, https://xgboost.readthedocs.io/en/latest/python/python_intro.html, https://catboost.ai/en/docs/, https://lightgbm.readthedocs.io/en/latest/index.html (accessed on 21 January 2022). |

3 | This information was available on the website: https://lightgbm.readthedocs.io/en/latest/Features.html#references (accessed on 21 January 2022). |

4 | Information about the payment of penalties by companies is available on: https://www.knf.gov.pl/o_nas/Kary_nalozone_przez_KNF (accessed on 21 January 2022). |

5 | The explanation of Elektrobudowa SA situation (in Polish) is available on: https://wysokienapiecie.pl/39649-elektrobudowa-idzie-pod-mlotek/ (accessed on 21 January 2022). |

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**Figure 1.**Histograms of the distributions of continuous variables after their transformation according to Formula (1).

**Figure 2.**Histogram of the X10 variable before (

**a**) and after (

**b**) transformation according to Formula (1).

**Figure 3.**Quantile–quantile plots of continuous independent variables after transformation according to Formula (1).

**Figure 4.**A plot of the Spearman rank correlation coefficient values between continuous independent variables.

**Figure 6.**Example plot of SHAP values for one iteration of the model evaluation process for the CatBoost algorithm.

**Figure 7.**The values of the Spearman rank coefficient of correlation between the positions of the independent variables in the feature importance rankings based on SHAP values for different machine learning methods.

Year | Number of Companies |
---|---|

2017 | 305 |

2018 | 311 |

2019 | 312 |

**Table 2.**Number and percentage of companies included in the analysis and classified as “bad” by year.

Year | Number of “Bad” | Percentage of “Bad” [%] |
---|---|---|

2017 | 93 | 30.49 |

2018 | 95 | 30.55 |

2019 | 96 | 30.77 |

Variable | Variable Name | Character of Variable |
---|---|---|

X1 | Net profit | Dichotomous |

X2 | Return on sales | Continuous |

X3 | Return on equity | Continuous |

X4 | Return on assets | Continuous |

X5 | Operating cash flow margin | Continuous |

X6 | Current Ratio | Continuous |

X7 | Quick Ratio | Continuous |

X8 | Absolute liquidity ratio | Continuous |

X9 | Debt ratio | Continuous |

X10 | Debt to equity ratio | Continuous |

X11 | Long-term debt to equity ratio | Continuous |

X12 | Operating profit margin | Continuous |

X13 | Sales profit margin | Continuous |

X14 | Basic earning power ratio | Continuous |

X15 | Net income to operating cash flow | Continuous |

X16 | Indicator of overall financial standing | Continuous |

X17 | Receivables to payables coverage ratio | Continuous |

X18 | Return on investment | Continuous |

X19 | Investment turnover ratio | Continuous |

Category | Number of Occurrences | Percentage of Occurrences [%] |
---|---|---|

0—loss | 263 | 28.34 |

1—profit | 665 | 71.66 |

Variable | Mean | Minimum Value | Maximum Value | Median | Coefficient of Variation [%] | Skewness Coefficient |
---|---|---|---|---|---|---|

X2 | −1387.96 | −1,216,550.00 | 445,611.11 | 2.94 | −3123.11 | −22.71 |

X3 | 13.76 | −5658.89 | 7278.58 | 7.70 | 3464.02 | 6.96 |

X4 | −6.78 | −7758.00 | 6325.71 | 3.05 | −5122.08 | −5.74 |

X5 | −480.07 | −246,550.00 | 5228.21 | 5.79 | −1783.38 | −26.17 |

X6 | 3.35 | 0.04 | 358.67 | 1.41 | 438.60 | 17.99 |

X7 | 2.86 | 0.03 | 358.67 | 1.01 | 512.24 | 18.20 |

X8 | 1.95 | 0.00 | 358.67 | 0.32 | 730.08 | 19.56 |

X9 | 55.73 | 0.28 | 2262.17 | 47.92 | 188.37 | 16.80 |

X10 | 129.55 | −15,158.62 | 16,453.24 | 89.90 | 692.44 | 2.04 |

X11 | 46.34 | −686.19 | 3314.26 | 18.74 | 388.58 | 12.59 |

X12 | −986.23 | −699,000.00 | 162,711.11 | 4.74 | −2496.28 | −24.90 |

X13 | −581.19 | −233,300.00 | 361.05 | 4.23 | −1761.10 | −21.28 |

X14 | −1.86 | −3998.00 | 2309.78 | 4.54 | −8464.50 | −14.40 |

X15 | 20,047.12 | −35,700.00 | 18,374,400.00 | 46.37 | 3008.83 | 30.36 |

X16 | −22.47 | −13,123.06 | 3202.08 | 0.99 | −2307.00 | −20.48 |

X17 | 0.91 | 0.00 | 56.19 | 0.59 | 245.68 | 17.60 |

X18 | −1.00 | −292.41 | 146.86 | 0.20 | −1859.29 | −8.05 |

X19 | 36.83 | −2.99 | 3866.35 | 7.99 | 474.30 | 14.70 |

**Table 6.**Values of skewness coefficient for continuous independent variables after transformation according to Formula (1).

X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 | X10 |

−1.20 | −0.86 | −0.84 | −1.37 | 1.05 | 1.05 | 0.22 | −1.19 | −3.21 |

X11 | X12 | X13 | X14 | X15 | X16 | X17 | X18 | X19 |

−0.94 | −1.43 | −1.58 | −1.09 | −0.79 | −1.51 | −0.85 | −0.15 | −1.04 |

X5 | X6 | X8 | X10 | X11 | X13 | X14 | X15 | X16 | X17 | X18 | X19 |
---|---|---|---|---|---|---|---|---|---|---|---|

0.0000 | 0.0000 | 0.0197 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.5602 | 0.2839 | 0.0000 | 0.0000 |

Year | Companies | “Bad” |
---|---|---|

2017 | 305 | 93 |

2018 | 311 | 95 |

2019 | 312 | 96 |

**Table 9.**Number of observations by category of the dependent variable and group based on quartiles of revenue volumes in 2017.

Category | I Group | II Group | III Group | IV Group |
---|---|---|---|---|

0 | 67 | 55 | 43 | 47 |

1 | 10 | 21 | 33 | 29 |

**Table 10.**Number of observations by category of the dependent variable and group based on quartiles of revenue volumes in 2018.

Category | I Group | II Group | III Group | IV Group |
---|---|---|---|---|

0 | 69 | 54 | 44 | 49 |

1 | 9 | 24 | 33 | 29 |

**Table 11.**Number of observations by category of the dependent variable and group based on quartiles of revenue volumes in 2019.

Category | I Group | II Group | III Group | IV Group |
---|---|---|---|---|

0 | 73 | 51 | 43 | 49 |

1 | 5 | 27 | 35 | 29 |

Character of Set | Category | Number of Records |
---|---|---|

Training set | 1 | 206 |

0 | 478 | |

Test set | 1 | 78 |

0 | 166 |

**Table 13.**Number of records by set type and category of dependent variable after stratification and SMOTE method.

Character of Set | Category | Number of Records |
---|---|---|

Training set | 1 | 478 |

0 | 478 | |

Test set | 1 | 78 |

0 | 166 |

**Table 14.**Mean value of AUC and Cohen’s kappa coefficients for the applied supervised learning methods after a 10-fold division of the sample into a training set and a test set and running the specified method.

Method | AUC | Cohen’s Kappa |
---|---|---|

Logistic regression | 0.6522 | 0.1903 |

Decision tree | 0.5913 | 0.1767 |

XGBoost | 0.7159 | 0.2754 |

Gradient boosting | 0.7100 | 0.2925 |

LightGBM | 0.7178 | 0.2716 |

CatBoost | 0.7321 | 0.3027 |

**Table 15.**Standard deviation value of AUC and Cohen’s kappa coefficients for the applied supervised learning methods after a 10-fold splitting of the sample into a training set and a test set and running the specified method.

Method | Standard Deviation of AUC | Standard Deviation of Cohen’s Kappa |
---|---|---|

Logistic regression | 0.0244 | 0.0425 |

Decision tree | 0.0347 | 0.0657 |

XGBoost | 0.0194 | 0.0162 |

Gradient boosting | 0.0181 | 0.0319 |

LightGBM | 0.0210 | 0.0566 |

CatBoost | 0.0195 | 0.0393 |

Ranking | Variable |
---|---|

1 | X11 |

2 | X17 |

3 | X14 |

4 | X10 |

5 | X19 |

6 | X13 |

7 | X8 |

8 | X6 |

9 | X18 |

10 | X5 |

11 | X16 |

12 | X15 |

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**MDPI and ACS Style**

Szymura, A.
Risk Assessment of Polish Joint Stock Companies: Prediction of Penalties or Compensation Payments. *Risks* **2022**, *10*, 102.
https://doi.org/10.3390/risks10050102

**AMA Style**

Szymura A.
Risk Assessment of Polish Joint Stock Companies: Prediction of Penalties or Compensation Payments. *Risks*. 2022; 10(5):102.
https://doi.org/10.3390/risks10050102

**Chicago/Turabian Style**

Szymura, Aleksandra.
2022. "Risk Assessment of Polish Joint Stock Companies: Prediction of Penalties or Compensation Payments" *Risks* 10, no. 5: 102.
https://doi.org/10.3390/risks10050102